System and method for estimating cell center position for cell ID based positioning

ABSTRACT

Systems and methods for estimating a cell center location in a wireless communication system having an interface to a satellite positioning system (“SPS”) such as for example, a Geosynchronous Positioning System (“GPS”). The wireless communication system provides service to mobile stations within a cell, each mobile station includes a SPS receiver. Examples of the systems and methods for estimating a cell center location analyze the mobile station locations in a cell as a uniform distribution of mobile station locations and calculate a statistical measure characterizing the mobile station locations as a function of the mobile station locations. In one example, the statistical measure is a maximum likelihood mobile station location. In another example, the statistical measure is the mean mobile station location in the cell. The estimated cell center location may be used to approximate the location of the mobile station during a warm or cold restart of the SPS receiver part of the mobile station.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 10/489,225, filed Sep. 10, 2002 now U.S. Pat. No. 7,672,675,titled “System of Utilizing Cell Information to Locate a WirelessDevice,” which claims priority under Section 119(e) to U.S. ProvisionalApplication Ser. No. 60/318,806, filed Sep. 10, 2001, each of which areincorporated into this application by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to positioning systems, and moreparticularly, to using wireless communications systems to provide aidinginformation to a positioning system.

2. Related Art

In densely built urban areas, the use of a positioning system such as aSatellite Positioning System (SPS)—for example, a Global Position System(GPS), also known as NAVSTAR—is often not available or reliable due tovarious reasons such as, for example, multipath, shadowing, and pathloss. In many situations, however, a GPS receiver may be associated witha cell of a cellular communication network and the base station servingthat particular cell. Accordingly, one method for mobile phonepositioning is to use the cell area coverage information (Cell ID) ofthe caller as a coarse location estimate to obtain the approximatelocation of the caller. In urban areas, cell position accuracy may be asclose as 100 meters, and therefore the center of a cell can be employedas the alternative position when GPS positioning has a larger error oris not available. The cell ID information is usually or always availableand reliable, and is independent of GPS measurements, and can also beeasily obtained by paging or updating. Thus, the center of a cell may beemployed as an approximate location of a mobile communication devicelocated within that cell.

While the location of the center of a cell may be available to mobiletelephone companies, it is usually not available to GPS locationproviders. Therefore, there is a need for providing systems or methodsfor making estimated cell center locations available to GPS locationproviders.

SUMMARY

According to one aspect of the subject matter disclosed, systems andmethods for estimating a cell center location provide the estimated cellcenter location as an approximate location for a SPS receiver in amobile station. Example systems for estimating a cell center location ina SPS system may include a SPS server connected to the SPS system toretrieve a plurality of mobile station locations from mobile stations ina cell in a wireless communication system, each mobile stationcomprising an SPS receiver. A SPS database stores the plurality ofmobile station locations and a cell identifier to identify the cell inwhich the mobile station is obtaining wireless communications service. Acell center location estimator calculates an estimated cell centerlocation by obtaining N mobile station locations assumed to be uniformlydistributed in a cell i and calculating a statistical measure of themobile station locations, where the statistical measure is either amaximum likelihood mobile station location or a mean mobile stationlocation.

Other systems, methods, features and advantages of the invention will beor will become apparent to one with skill in the art upon examination ofthe following figures and detailed description. It is intended that allsuch additional systems, methods, features and advantages be includedwithin this description, be within the scope of the invention, and beprotected by the accompanying claims.

BRIEF DESCRIPTION OF THE FIGURES

The invention can be better understood by referring to the followingfigures. The components in the figures are not necessarily to scale,emphasis instead being placed upon illustrating the principles of theinvention. In the figures, like reference numerals designatecorresponding parts throughout the different views.

FIG. 1 is a block diagram of an example of a system for providinglocation-based services;

FIG. 2 is a block diagram of a portion of the system illustrated in FIG.1;

FIG. 3 is a block diagram of the system in FIG. 1 illustrating operationof a positioning system and a wireless communications system;

FIG. 4 is a block diagram of a portion of the system illustrated in FIG.1 that implements examples of systems and methods for estimating a cellcenter in a wireless communication system;

FIG. 5A is a schematic diagram illustrating an example of a method forestimating a cell center;

FIG. 5B is a flowchart of an example of a method for estimating a cellcenter location;

FIG. 5C is an example of an X-Y graph showing locations of mobilestations in four example cells;

FIG. 6A is a schematic diagram illustrating another example of a methodfor increasing accuracy of an estimated cell center location;

FIG. 6B is a flowchart of another example of a method for estimating acell center location;

FIG. 7A is a schematic diagram illustrating another example of a methodfor increasing accuracy of an estimated cell center location;

FIG. 7B is a flowchart of another example of a method for estimating acell center location;

FIG. 8 is a schematic diagram illustrating another example of a methodfor estimating a cell center; and

FIG. 9 is a schematic diagram illustrating an example of another methodfor estimating a cell center.

DETAILED DESCRIPTION

In the following description, reference is made to the accompanyingdrawings that form a part hereof, and in which is shown by way ofillustration one or more specific exemplary embodiments in which theinvention may be practiced. It is to be understood that otherembodiments may be utilized and structural changes may be made withoutdeparting from the scope of this invention.

FIG. 1 is a graphical representation of three cell sites within acluster of cells of a cellular telephone network (known as the “cellularnetwork”). FIG. 1 illustrates a plurality of cells 100, 102 and 104 inthe cellular telephone network. Consistent with convention, each cell100, 102 and 104 is shown symbolically as having a hexagonal cellboundary. Within each cell 100, 102 and 104 are base stations 106, 108and 110 that are located near the center and/or centroid of thecorresponding cell 100, 102 and 104. Specifically, the base station 106is located within cell 100, the base station 108 is located within cell102, and the base station 110 is located within cell 104.

The boundaries 112, 114 and 116 separating the cells 100, 102 and 104generally represent an area where handoff occurs between the cells 100,102 and 104. As an example, when a wireless device 118 (also known as a“mobile unit” or “mobile station”) moves away from the base station 106in the cell 100 towards an adjacent base station 108 in the adjacentcell 102, the signal-to-interference plus noise ratio (“S/I+N”) from thebase station 106 will drop below a predetermined threshold level while,at the same time, the S/I+N from the second base station 108 increasesabove this predetermined threshold as the wireless device 118 moves overthe boundary 112 into the cell 102. Cellular systems are designed toprovide coverage from each base station within areas that roughlyoverlap at the boundaries 112, 114 and 116. In addition, wirelessdevices are designed to receive signals from various base stations andare capable of initiating a handoff if the signal level of one stationis stronger than the one currently being used for communication.

Each cell 100, 102 and 104 and its corresponding base station 106, 108and 110 is in signal communication with a cellular network server 120,via signal paths 122, 124 and 126, respectively. The cellular networkserver 120 is generally a switching network server that may includetelecommunication switches (not shown) and a central office (not shown).The cellular network server 120 controls the operation of the basestations 106, 108 and 110 and may assign individual cellularidentification values to the base stations 106, 108 and 110corresponding to the identification values for cells 100, 102 and 104.

These identification values may then be transmitted via a two-waychannel or a broadcast channel to individual wireless devices (such aswireless device 118) located in the cellular network and utilized foridentifying the location of the wireless device 118 relative to aspecific cell. As an example, when the base station 106 broadcasts acellular identification value (also known as a “cellular tag” or “cellID”) for cell 100, wireless device 118 would receive the broadcastsignal and respond to base station 106 identifying itself as wirelessdevice 118 located within the coverage area of cell 100. Thisidentification may take place at any time when the wireless device 118and base station 106 are communicating such as in the initial cellularhandshake procedure or at a later time. Accordingly, after the wirelessdevice 118 and base station 106 exchange this information, the wirelessdevice 118 contains the cell ID and the base station 106 contains anidentifier of the wireless device 118.

As another example, when base stations 106, 108, 110 broadcast theircellular identification value (also known as a “cellular tag”) for thecells 100, 102 and 104, the wireless device 118 would receive thebroadcast signals. These signals are sent through the base station 106(through which it is communicating) identifying itself as wirelessdevice 118 located within the coverage area of cell 100. Thisidentification may take place at any time when the wireless device 118and base station 106 are communicating such as in the initial cellularhandshake procedure or at a later time. During this exchange ofinformation, the cellular network server 120 registers the wirelessdevice 118 as being within cell 100 and communicating via base station106. The registration of the wireless device 118 may involve storing orlinking the cell ID of the base station 106 (and cell 100) with theidentifier of the wireless device 118 in a database within the cellularnetwork. When the wireless device 118 moves into another cell, thecellular network would update its database to link the wireless device118 to the cell ID of the cell it entered into. In examples of systemsand methods for aiding positioning systems consistent with the presentinvention, the cellular identification values may advantageously be usedas approximate location aids for the wireless device 118.

FIG. 2 is a block diagram illustrating an example of an implementationof a mobile unit location system (“MULS”) 200, which may receive SPSsignals from a SPS constellation 202. The MULS 200 may include a mobileunit (i.e., a wireless device) 204 and a cellular network server 206.The cellular network server 206 may include a base station 208, acentral office 210, an SPS continuous reference network 212, a database214, and an end user 216. The base station 208 may also be optionallyindependent of the cellular network server 206. The central office 210is in signal communication with the base station 208, SPS continuousreference network 212, database 214 and end user 216 via signal paths218, 220, 222 and 224, respectively. Additionally, the SPS continuousreference network 212 may be optionally in signal communication with thedatabase 214 via optional signal path 226.

The base station 208 is a fixed device that may include a cellular towerand the associated equipment with which the mobile unit 204 maycommunicate. The base station 208 communicates with a landline telephonenetwork (whether private or public) such as the plain old telephoneservice (“POTS”). The central office 210 (also known as a “publicexchange”) is generally a facility where lines of a subscriber arejoined to switching equipment for connecting with other subscriberswhether locally, or by long distance. The SPS continuous referencenetwork 212 is a fixed device and associated equipment for receiving SPSsignals from the SPS constellation 202 via signal path 225. The database214 may store location information of the mobile unit 204 withassociated information of a cell. The associated information of a cellmay include the cellular identification of the cell, as well ascharacteristic information of the cell measurable by a mobile unit inthe cell such as signal strength, bit error rate (BER), propagationdelay and/or multipath of the signal transmitted by the base station tothe mobile unit within the cell, the number of fingers in a rakereceiver and their relative delays and phases, and the like. Inaddition, in accordance with implementations described below, thedatabase 214 may also include estimated parameters of one or more cells,such as the mass center and radius of a cell. Such parameters may beupdated over time, and may be utilized for estimating the position of amobile unit within the cell such as the mobile unit 204. The end user216 may be any end user such as a program, application, utility,subsystem or actual individual that desires the location information ofthe mobile unit 204 including a user of the mobile unit 204.

The mobile unit 204 may include a SPS receiver 226 and a cellulartransceiver 228. The SPS receiver 226 receives SPS signals from the SPSconstellation 202 via signal path 230 and the cellular transceiver 228is in signal communication with the base station 208 via signal path232. Examples of the SPS receiver 226 include the SiRFstarI, SiRFstarIIand SiRFstarIII GPS receivers produced by SiRF Technology, Inc. of SanJose, Calif., the GPSOne GPS receiver produced by Qualcomm Incorporatedof San Diego, Calif., or any other GPS receiver capable of operationwithin the mobile unit 204. The cellular transceiver 228 (also known as“call processing function”) may be any radio frequency (“RF”), Amps,FDMA, TDMA, GSM, CDMA, W-CDMA, CDMA-2000 or UMTS type transceiver.

FIG. 3 is a block diagram illustrating a simplified example of animplementation of the MULS 300 in a typical cellular telephoneenvironment. The MULS 300 includes a mobile unit 302, a base station304, central office 306, SPS continuous reference network 308, database310 and end user 312. The mobile unit 302 may include a SPS client 314such as a SiRFLoc client and a call processing function 316 such as aRF, Amps, FDMA, TDMA, GSM, CDMA, W-CDMA, CDMA-2000 or UMTS typetransceiver. The base station 304 includes the fixed device such asradio tower 318 and the associated infrastructure 320. The centraloffice 306 includes an SPS server 322 such as SiRFLoc server and acentral office server 324. As an example, the central office server 324may include a Serving Mobile Location Center (SMLC)/Global MobileLocation Center (GMLC) as defined in the wireless location standard forGSM. The central office server 324 may include switching components andelectronics for performing the wireless telecommunications functions ofthe central office 306. The SPS continuous reference network 308includes a SPS reference receiver 326 and a SPS data center 328. The SPScontinuous reference network 308 and the mobile unit 302 both receiveSPS signals from the SPS constellation 330.

As an example of operation, the SPS continuous reference network 308collects data, from the SPS constellation 330 in the system coveragearea in real-time, and stores collected data locally in a memory unit(not shown) within the SPS continuous reference network 308. Based onthe coverage area, multiple reference receivers 326 may be used in thesystem. Periodically, the SPS server 322 polls, via signal path 332, thedata from the SPS continuous reference network 308 related to the SPSclient 314, and caches it in its internal memory unit (not shown) in theSPS server 322, so that it may be reused for another SPS client (notshown) without polling it again if it is relevant to subsequent SPSclients (not shown). This information is then transmitted to the SPSclient 314 via signal path 334, which is the signal path through thecentral office 306, base station 304 and call processing function 316.

It is appreciated that the combining of cellular identificationinformation with the mobile unit 302 location may take place eitherwithin the SPS subsystem (i.e., the SPS client) 314 or within the callprocessing function 316 or even in the SPS server 322. In the oneexample, the cellular identification information is transferred from thecall processing function 316 to the SPS client 314 and tagged to thecomputed position (i.e., latitude, longitude and altitude data). Inanother example, the location from the SPS client 314 is sent to thecall processing function 316 where it is tagged to the cellularidentification information. This tagged data is then sent as a message,over the wireless network, to database 310 where it is stored. In athird example, the location from the SPS client 314 and the cellularidentification information are received as different messages from thesame SPS client 314 during the same geolocation session, and associatedtogether at the SPS server 322.

The MULS 300 advantageously provides the mobile unit 302 with additionalsurrounding information (i.e., an approximate location aid) from thedatabase 310. As a result of providing this approximate location aid, aSPS receiver may be jump-started to provide position information for themobile unit 302 more quickly. Knowing the approximate location of themobile unit 302 also helps the mobile unit 302 expedite its locationcalculations.

Three general situations may apply to a given mobile unit located in agiven cell when the mobile unit or a remote party desires to know theposition of the mobile unit. First, the GPS location of the mobile unitmay be available due to, for example, the proper functioning of the GPScomponents embedded with the mobile unit. In this case, the mobile unitdoes not require positioning assistance. Second, GPS locationinformation may be available, but is determined to be unreliable due toinaccuracy or uncertainty. In this case, the mobile unit may requireposition assistance information if the position assistance informationavailable at the time is determined to be more reliable than the GPSlocation information. Third, the GPS location of the mobile unit may benot available at all due to, for example, a failure of the GPScomponents embedded with the mobile unit. In this case, the mobile unitrequires position assistance information to calculate its position. Inthe implementations described by way of example below and illustrated inthe drawings, position assistance information may include the estimatedcenter of the cell in which the mobile unit is located. The actuallocation of the center of a cell is not needed to provide cell ID basedpositioning. Likewise, the actual location of the base station is notneeded. As previously noted the base station may not be located at thecenter of the cell and thus is not necessarily the best estimate of thelocation of a mobile device within the cell. Thus, the implementationsdescribed and illustrated below are operative in situations where thelocation of the cell center is not available.

FIG. 4 is a schematic diagram illustrating use of systems and methodsfor estimating cell center locations to acquire coarse locationestimates to an SPS receiver that is unable to obtain its position withsuitable accuracy and precision, or is attempting to locate itself onstartup. The diagram in FIG. 4 shows three adjacent cells, a first cell400, a second cell 402, and a third cell 404. Each cell is serviced by afirst base station 406 in the first cell 400, a second base station 408in the second cell 402, and a third base station 410 in the third cell404.

The base stations 406, 408, 410 provide service to the mobile stationsin their respective cells. The first base station 406 provides serviceto mobile stations MSA 430, MSB 431, and MSC 432 in cell 400. The secondbase station 408 provides service to mobile stations MSD 433, MSE 434,and MSF 435 in cell 402. The third base station 410 provides service tomobile stations MSG 436, MSH 437, and MSI 438 in cell 404. Each basestation 406, 408, 410 may be connected via a variety of signal paths andcombinations of signal paths (some of which are described above withreference to FIGS. 1-3) to a SPS server 422. The SPS server 422 includesan interface to a SPS database 410 and an interface to a cell centerestimator 424. The SPS server 422 may receive location information andcell ID information from the mobile stations in the cells as describedabove with reference to FIGS. 1-3. The SPS database 410 may receive andstore the location information including cell ID information for eachmobile station in each cell. The location and cell ID information in theSPS database 410 may be accessed and used by a cell center estimatingfunction to estimate the location of the center of the cell.

In examples of systems and methods for estimating cell center locations,the SPS database 410 may include data for each mobile station in eachcell serviced by the SPS server 322. Table 1 shows examples of the datathat may be included in the SPS database 410.

TABLE 1 Estimated Mobile Mobile Station Horizontal Cell Cell Center CellStation Id Position Variance (V_(j)) Identifier Location Radius MSA x₀,y₀ $\begin{bmatrix}\sigma_{N,0}^{2} & \sigma_{{NE},0}^{2} \\\sigma_{{NE},0}^{2} & \sigma_{E,0}^{2}\end{bmatrix}_{j = 0}$ C₁ {circumflex over (X)}₁, Ŷ₁ R1 MSB x₁, y₁$\begin{bmatrix}\sigma_{N,1}^{2} & \sigma_{{NE},1}^{2} \\\sigma_{{NE},1}^{2} & \sigma_{E,1}^{2}\end{bmatrix}_{j = 1}$ C₁ {circumflex over (X)}₁, Ŷ₁ R1 MSC x₂, y₂$\begin{bmatrix}\sigma_{N,2}^{2} & \sigma_{{NE},2}^{2} \\\sigma_{{NE},2}^{2} & \sigma_{E,2}^{2}\end{bmatrix}_{j = 2}$ C₁ {circumflex over (X)}₁, Ŷ₁ R1 MSD x₃, y₃$\begin{bmatrix}\sigma_{N,3}^{2} & \sigma_{{NE},3}^{2} \\\sigma_{{NE},3}^{2} & \sigma_{E,3}^{2}\end{bmatrix}_{j = 3}$ C₂ {circumflex over (X)}₂, Ŷ₂ R2 MSE x₄, y₄$\begin{bmatrix}\sigma_{N,4}^{2} & \sigma_{{NE},4}^{2} \\\sigma_{{NE},4}^{2} & \sigma_{E,4}^{2}\end{bmatrix}_{j = 4}$ C₂ {circumflex over (X)}₂, Ŷ₂ R2 MSF x₅, y₅$\begin{bmatrix}\sigma_{N,5}^{2} & \sigma_{{NE},5}^{2} \\\sigma_{{NE},5}^{2} & \sigma_{E,5}^{2}\end{bmatrix}_{j = 5}$ C₂ {circumflex over (X)}₂, Ŷ₂ R2 MSG x₆, y₆$\begin{bmatrix}\sigma_{N,6}^{2} & \sigma_{{NE},6}^{2} \\\sigma_{{NE},6}^{2} & \sigma_{E,6}^{2}\end{bmatrix}_{j = 6}$ C₃ {circumflex over (X)}₃, Ŷ₃ R3 MSH x₇, y₇$\begin{bmatrix}\sigma_{N,7}^{2} & \sigma_{{NE},7}^{2} \\\sigma_{{NE},7}^{2} & \sigma_{E,7}^{2}\end{bmatrix}_{j = 7}$ C₃ {circumflex over (X)}₃, Ŷ₃ R3 MSI x₈, y₈$\begin{bmatrix}\sigma_{N,8}^{2} & \sigma_{{NE},8}^{2} \\\sigma_{{NE},8}^{2} & \sigma_{E,8}^{2}\end{bmatrix}_{j = 8}$ C₃ {circumflex over (X)}₃, Ŷ₃ R3

In Table 1, the Mobile Station Id may be any suitable identifier thatuniquely identifies the mobile stations in each cell. The Mobile StationId is shown symbolically as MSA, MSB, MSC, MSD, MSE, MSF, MSG, MSH, andMSI in Table 1. Actual Id's may include the mobile station cellulartelephone number assigned to each mobile station, an IP address, or anyother suitable identifier. The mobile station position in Table 1includes latest positions calculated for each mobile station. Eachmobile station shown in Table 1 includes a SPS client and operates inthe positioning system as described above. During operation, the mobilestation position is periodically updated by the SPS positioning system.

The SPS positioning system may also calculate a horizontal varianceV_(j) for the mobile station (j). The horizontal variance V_(j) is thevariance of the location of the mobile station j in a flat,two-dimensional (x,y) space defining the area of the cell relative toits true position. The horizontal variance may be calculated as a 2×2symmetrical matrix including an SPS positioning variance along the northaxis (i.e. σ_(N) ²), an SPS positioning variance along the east axis(i.e. σ_(E) ²), and a variance relative to both axes (i.e. σ_(NE) ²).The SPS positioning variances, σ_(N) ², σ_(E) ², σ_(NE) ², aredetermined during acquisition of a location by the mobile stations andavailable when the mobile station locations become available.

Table 1 also includes a cell identifier, which may be a unique number,alphanumeric sequence, or other suitable symbol or token for identifyingthe cell. The Cell identifier may be provided by the wirelesstelecommunications system as described above.

Also as shown in Table 1, the database may include an estimated cellcenter location. The estimated cell center location is a calculatedestimate of the cell center location, which is a center of the areaserviced by the cell. The estimated cell center location may not be theexact true center of the service area of the cell; it may only be anapproximation sufficiently accurate for use as an estimated location fora mobile station in the cell. In systems and methods for estimating thecell center location, the cell center estimator 424 uses the locationsof mobile stations (as determined by the SPS positioning system)serviced by the cell to estimate the center of the cell as describedbelow. The cell center estimator 424 may obtain the mobile stationlocation from a database such as the SPS database 410.

The cell radius in Table 1 may be periodically calculated and/or updatedeach time an estimated cell location is determined. The cell radius maybe calculated as one step in determining the estimated cell centerlocation. The calculated cell radius may then be used as described belowto determine a more accurate estimated cell location, which may be usedto update the cell radius. The cell radius may be initially calculatedwithout a starting cell center location by starting with the positionsof all of the mobile stations in the cell and mapping an area covered bythe mobile stations at the locations. A circle may be defined around thearea that includes all of the mobile stations. The shape of the cell 504is of no real significance. The actual shape of a cell is actuallydefined by the outward distances to which a cell is able to provideservice to a mobile station. Cells may actually overlap in coverage. Thecell shape is defined as circular as a first step in the process. Aninitial circle radius may be defined as a distance just greater thanhalf of the largest distance between any two mobile stations.

During operation, the mobile station may not be able to obtain aposition, whether not at all, or with a desired accuracy. Also, if themobile station is turned off, or its positioning capability is disabled,the mobile station position in the database may not be accurate when themobile station is re-initialized. Such a mobile station may take thelast estimated cell center location and use it as its own location.

In FIG. 4, the cell center location for cell 1 is {circumflex over(X)}₁, Ŷ₁, the cell center location for cell 2 is {circumflex over(X)}₂,Ŷ₂, and the cell center location for cell 3 is {circumflex over(X)}₃,Ŷ₃. As described graphically in FIG. 4, the cell center locationsdo not coincide with the base stations. The following describes systemsand methods for estimating a cell center location to set as the celllocation, which may be used by a mobile station served by the cell asits location when the mobile station is unable to obtain its ownlocation, or is initializing its positioning capabilities. As describedbelow, the estimated cell center location is a derived locationcalculated from statistical measures of the mobile station locations inthe cell. The statistical measures are based on assumptions about thedistribution of the mobile stations in the cell. In one example below,the statistical measure selected for estimating a cell center locationis a maximum likelihood mobile station location based on a Gaussiandistribution for mobile station locations with a large variance. Inanother example, the mean of the mobile station locations is selected asthe statistical measure. Those of ordinary skill in the art willappreciate that other measures may be used.

An example cell 504 is illustrated in FIG. 5A as a circle. For purposesof estimating a cell center position, a function (such as the cellcenter estimator 424 in FIG. 4) may obtain mobile station location datain a cell from a database such as the SPS database 410 in FIG. 4. Thedata for each mobile station served by a target cell (i.e. cell 504) maybe retrieved and modeled as a circle as shown in FIG. 5 in which theperimeter of the circle is a cell border 508, the center of the circleis an estimated cell center (or cell location) 512, and the smallcircles inside the cell border 508 are mobile stations 510 served by thecell contained in the cell border 508, where each mobile station 510 isalso an SPS receiver. The radius R in FIG. 5 is the initial cell radiuscalculated as described above. The mobile stations 510 are assumed to beuniformly distributed within the cell border 508. Thus, the SPS positionestimate for each mobile station is assumed to be a Gaussiandistribution with the true position being the mean with a varianceV_(j).

In accordance with the notation below, j is a mobile station (i.e. SPSreceiver) and i identifies a cell. The initial radius of the cell is r₀in the equations below. The positions of the SPS receivers are definedas x, y coordinates along north and east axes. The variance V_(ij) ofthe true position of a SPS receiver relative to an estimated cell centermay be calculated as follows.

$\begin{matrix}{V_{ij} = {\begin{bmatrix}\sigma_{tj}^{2} & 0 \\0 & \sigma_{tj}^{2}\end{bmatrix} + V_{j}}} & (1)\end{matrix}$

The value σ_(tj) ² is the variance of the SPS receiver's true positionrelative to the true cell center. The value σ_(tj) ² may be determinedin a variety of ways. The true value of σ_(tj) ² in a given cell may beassumed to be relatively large since very little is known about the trueposition of the cell center. In one example, σ_(tj) ² may be defined tobe σ_(tj) ²=(r₀/2)². The variance V_(j) is a 2×2 matrix that may beretrieved from the database (an example of which is shown in Table 1).The equation for V_(ij) then becomes:

$\begin{matrix}{V_{ij} = {\begin{bmatrix}\left( {r_{oij}/2} \right)^{2} & 0 \\0 & \left( {r_{oij}/2} \right)^{2}\end{bmatrix} + V_{j}}} & (2)\end{matrix}$Based on Eq. (2), the estimated cell center location X_(ci) may bedetermined to be the maximum likelihood location according to:

$\begin{matrix}{{\hat{X}}_{ci} = {\left\lbrack {\sum\limits_{j = 1}^{N}\; V_{ij}^{- 1}} \right\rbrack^{- 1}{\sum\limits_{j = 1}^{N}\;{V_{ij}^{- 1}{\hat{X}}_{j}}}}} & (3)\end{matrix}$where {circumflex over (X)}_(j) is the true position of each mobilestation j, assumed to be the position calculated by the SPS positioningsystem.

Equations (2) and (3) may be re-written to provide an approximateaccuracy for the estimate of the position based on a certain number ofSPS receivers, or to calculate the number of SPS receivers needed toachieve a certain accuracy of the cell location estimate (which is alsothe coarse location accuracy when SPS signal is not available).

$\begin{matrix}{{{If}\mspace{14mu}\sigma_{tj}^{2}\text{>>}\sigma_{N}^{2}\mspace{14mu}{and}\mspace{14mu}\sigma_{tj}^{2}\text{>>}\sigma_{E}^{2}},} & \; \\{V_{ij} = {{\begin{bmatrix}\sigma_{tj}^{2} & 0 \\0 & \sigma_{tj}^{2}\end{bmatrix} + V_{j}} \approx \begin{bmatrix}\sigma_{tj}^{2} & 0 \\0 & \sigma_{tj}^{2}\end{bmatrix}}} & (4)\end{matrix}$Then, the cell location can be approximated using the mean mobilestation location and sample variance as:

$\begin{matrix}{{\hat{X}}_{ci} \approx {\frac{1}{N}{\sum\limits_{j = 1}^{N}{\hat{X}}_{j}}}} & (5)\end{matrix}$

$\begin{matrix}{{{var}\left( {\hat{X}}_{ci} \right)} \approx {\frac{1}{N}\begin{bmatrix}\sigma_{tj}^{2} & 0 \\0 & \sigma_{tj}^{2}\end{bmatrix}}} & (6)\end{matrix}$The variance in one axis given the assumption above for Equation (4) is:

$\begin{matrix}{{\sigma_{ci}^{2} \approx {\frac{1}{N}\sigma_{tj}^{2}}}{or}} & (7) \\{\sigma_{ci} \approx \frac{\sigma_{tj}}{\sqrt{N}}} & (8)\end{matrix}$The number of mobile stations needed in a cell to estimate the cellcenter to a desired accuracy may be determined using:

$\begin{matrix}{N \approx \left( \frac{\sigma_{tj}}{\sigma_{ci}} \right)^{2}} & (9)\end{matrix}$

The equations (1)-(5) above may be implemented in hardware/softwarefunctions, For example, the cell center estimator 424 that may operatein the SPS server 422 as shown in FIG. 4, for example. The cell centerestimator 424 may operate as part of the SPS server 422 or incommunication with the SPS server 422. The cell center estimator 424 mayoperate periodically to keep the estimated cell center location updatedas the number of GPS receivers increases or decreases within the cell.In one example, the cell center estimate is updated along with anapproximation of the accuracy of the estimate. The estimated locationmay then be updated when the approximate accuracy increases beyond thepreviously calculated accuracy.

FIG. 5B is a flowchart of an example of a method 500 for determining anestimated cell center location. The method 500 in FIG. 5B may beperformed in software by a function such as the cell center estimator424 with access to an SPS database with a structure similar to thatshown in Table 1. In the method 500, the locations of each of N mobilestations in the cell of interest (i) as determined by the SPSpositioning system are accessed as shown in step 520. The mobile stationlocations may be accessed from a database, such as the SPS database 410described above with reference to FIG. 4. FIG. 5B includes an ORfunction block 521 indicating that the method may proceed in one of twoways. The method may continue from Step 520 to Step 522 or from Step 520to Step 534. Examples of the method 500 in FIG. 5B may include bothpaths, or one or the other. If the method 500 proceeds to Step 522, thelongest distance between any two mobile stations is determined in Step522. The longest distance may be determined by calculating the distancebetween all of the mobile stations and selecting the largest distance.The two mobile stations that are farthest from each other may be assumedto be at opposite edges of the cell. In step 524, an initial cell radiusis defined as half the distance between the two mobile stations that arefarthest from each other. In step 526, the initial radius of the cell isused to calculate the value σ_(tj) ², which is the variance of the SPSreceiver's true position relative to the true cell center. This value isdetermined for each mobile station in the cell. In step 528, the SPSvariance relative to the true position for each mobile station in thecell (V_(j)) may be retrieved from the database. At step 530, thevariance V_(ij) of the mobile station relative to the estimated cellcenter location is calculated using, for example, equation (2) above foreach mobile station. In step 532, the variance V_(ij) for each mobilestation, and the location of each mobile station ({circumflex over(X)}_(j)) are used to calculate the estimated cell center location usingequation (3) above, which calculates the maximum likelihood mobilestation location in the cell.

If at OR function block 521 the method 500 proceeds to step 534, thenthe mobile station locations obtained in Step 520 are used to calculatea mean mobile station location according to Equation (5) above.Additional steps may be performed to determine the accuracy given thenumber of mobile station locations used, or to determine the number ofmobile stations required to obtain a desired accuracy as described abovein Equations (8) and (9).

The estimate of the cell center location may be made more accurate byfiltering the mobile station locations used in estimating the cellcenter location to exclude mobile station locations that may not fitwith the assumption that the mobile stations are uniformly distributed.FIG. 6A shows one example of a mobile station location filter in which acell 604 is again illustrated as a circle 608 having a radius ‘r’ (whichmay be r₀) and containing mobile stations 610 served by the cell. Aninitial cell center estimate 612 at the center of the circle 608 may bedetermined using examples of methods described above with reference toFIGS. 5A & 5B. In an example of a method for increasing the accuracy ofthe cell center estimate, a more accurate cell center estimate may bedetermined by redefining the circle 608 with a minimum radius ‘r’ thatwould encircle a certain percentage of the mobile stations 610 served bythe cell 504. The percentage may be selected according to a desiredaccuracy level in view of Equation (9) above for the number ‘N’ ofmobile stations required to obtain a desired accuracy level. In themethod illustrated by FIG. 6A, reducing the coverage area may eliminatethe effect that outliers may have on the accuracy of the cell centerestimate. Outliers would include outlier mobile stations 620 that aresufficiently far from the rest of the mobile stations that the positionswould make the distribution of the mobile stations less uniform.

FIG. 5C shows an X-Y graph showing example mobile stations locationsplotted on X-Y coordinates for four example cells. The cells in FIG. 5Care a first cell 550, a second cell 552, a third cell 554 and a fourthcell 556. The legend indicates where in the graph are located: a truecell position (for each of the four cells), a maximum likelihood cellestimate, the GPS locations for mobile stations in the first cell 550,the GPS locations for mobile stations in the second cell 552, the GPSlocations for mobile stations in the third cell 554, and the GPSlocations for mobile stations in the fourth cell 556. The graph in FIG.5C illustrates how mobile station locations may be mapped in cells

In the example shown in FIG. 6A, the radius is minimized so as to covera percentage (e.g. 95%) of the mobile stations (i.e. SPS receivers) inthe cell 604. As shown in FIG. 6A, a radius ‘r’ may be defined bydetermining the distance of each of the mobile stations from the initialcell center estimate 612 using the mobile station location information.An initial radius ‘r’ may be defined as the distance from the initialestimated cell center to the most distant mobile station. The radius maythen be reduced and compared with the distances of the mobile stationsuntil the desired percentage of mobile stations are within a minimumradius. The locations of the mobile stations within the circle definedby the minimum radius ‘r’ may then be used in the equations above todetermine another cell center estimate. The process may be periodicallyperformed to adjust the cell center estimate to be more accurate. If thecell radius is stored in the database, the cell radius may be updatedeach time the cell center estimate is adjusted.

FIG. 6B is a flowchart of a method 600 for obtaining a more accurateestimate of the cell center location. The method 600 illustrated by inFIG. 6B may be performed in the cell center estimator 424 (in FIG. 4)and may be performed subsequent to the method 500 illustrated in FIG.5B. The method 600 includes step 630 in which the locations (asdetermined by the SPS positioning system) of all N mobile stations maybe retrieved from a storage element (such as a database with a structuresimilar to that of Table 1). At step 632, the method determines thedistance of each mobile station from the estimated cell center X_(ci) ascalculated for example, by using method 500 in FIG. 5B. At step 634, themethod 600 searches for the distance between the estimated cell centerlocation and the mobile station that is farthest away from the estimatedcell center location. This distance is defined as the new initial cellradius (r₀). In step 636, a minimized cell radius (r₁) is calculated asr₁=P % of r₀ and in step 636, or in a separate step, a loop counter isinitialized to 1. At decision block 638, a test is performed todetermine if the circle defined by radius r₁ encompasses P % of themobile stations in the cell. If the test determines that YES, P % of themobile stations are in the circle defined by r₁, then the cell radius r₀is set to r₁ at step 640. At step 642, the calculation of the estimatedcell center as performed using method 500 in FIG. 5B is repeated usingthe new cell radius r₁.

If at decision block 638, P % of the mobile stations in the cell are notwithin the circle defined by r₁, then at decision block 644 a secondtest is performed to determine if fewer than P % of the mobile stationsin the cell are within the circle defined by r₀. If fewer than P % ofthe mobile stations are within the circle defined by r₁, then r₁ isincreased by a predetermined value Δr/1 at step 646 to make the circlebigger. If decision block 644 determines that the number of mobilestations in the circle defined by r₁ is not fewer than P % of the mobilestations then it is greater than P % of the mobile stations. At step648, the radius is decreased by a value Δr/1. The method 600 in FIG. 6Bmay loop at decision blocks 638 and 644 so that it may take many passesthrough decision blocks 638 and 644 to get to a radius for a circle thatencompasses P % of the mobile stations. The loop counter, 1, isincremented at step 650 each time the loop is executed to decrease theincremental amount that the radius is increased or decreased.

The method 600 in FIG. 6B may augment the method 500 of FIG. 5B todetermine a more accurate cell center location by filtering the samplesize to include the mobile stations that are more uniformly distributed;that is, by removing any outliers that may limit the validity ofassuming that the mobile stations are uniformly distributed. Anotherexample of a method for increasing accuracy of a cell center estimate isshown in FIGS. 7A & 7B. In FIG. 7A, a cell 704 is again illustrated as acircle 708 with an initial cell center estimate 712. The cell 704 servesa number of mobile stations 710. In the example shown in FIG. 7A, thedistance of the most distant mobile station in a percentage of themobile stations served by the cell is minimized to remove the effect ofoutlier mobile stations 720. The maximum distance in the percentage ofmobile stations may be minimized by first determining the distance ofeach of the mobile stations from the initial cell center estimate 712using the mobile station location information. The distances of themobile stations are then analyzed by selecting the desired percentage ofmobile stations that are closest to the estimated cell center location.The cell center estimator 424 may then re-calculate an estimated cellcenter using the mobile station locations for the selected percentage ofthe mobile stations. The process may be periodically performed to adjustthe cell center estimate to be more accurate. If the cell radius isstored in the database, the cell radius may be updated each time thecell center estimate is adjusted.

FIG. 7B is a flowchart of a method 700 for increasing accuracy of a cellcenter estimated location. The method 700 illustrated by in FIG. 7B maybe performed in the cell center estimator 424 (in FIG. 4) and may beperformed subsequent to the method 500 illustrated in FIG. 5B and/or themethod 600 illustrated in FIG. 6B. The method 700 includes step 730 inwhich the locations (as determined by the SPS positioning system) of allN mobile stations may be retrieved from a storage element (such as adatabase with a structure similar to that of Table 1). At step 732, themethod determines the distance of each mobile station from the estimatedcell center X_(ci) as calculated for example, by using method 500 inFIG. 5B, or by method 600 in FIG. 6B. At step 734, the method 700searches for the distance between the estimated cell center location andthe mobile station that is farthest away from the estimated cell centerlocation. This distance is defined to be an initial cell radius r₀. Atstep 736, a function is performed to determine the distance between theestimated cell center Xci and the mobile station that is closest to aradius, r1, that defines a circle that encompasses P % of the mobilestations in the cell. For example, this may be done by arranging the Nmobile stations in order from closest to farthest relative to theestimated cell center location. Then the first P % of the N mobilestations are identified to be within circle defined by the reduced cellradius. A radius r₁ is then defined to be the cell radius at step 740.At step 742, the calculation of the estimated cell center location usingmethod 500 in FIG. 5B may then be performed using only the P % of themobile stations identified in step 736.

In some cases, it may not be possible to assume a uniform distributionof mobile stations in a cell. FIG. 8 schematically illustrates a cell804 defined as a rectangle 808 in which mobile stations are distributedin three clusters 810. Each cluster 810 may be analyzed by assuming eachcluster 810 is evenly distributed and using the mobile station locationinformation in each cluster 810 in equations (2) and (3), or in equation(5) above to determine an estimated center for each cluster 812, 813,814. To determine if the mobile station locations map out in clusters, amethod may calculate an initial cell radius as described above for theentire cell. The method may then take fractional parts of the initialcell radius (e.g. ½, ⅓, ¼) and use the parts to draw circles in randomlocations within the cell. The areas within these circles may then beanalyzed to determine the number of mobile station locations within theareas and whether the number is sufficient to provide a reasonablyaccurate estimate of a center location for the circles. Such a methodmay use equations (7), (8), and (9) above to determine the adequacy ofthe circle areas being analyzed. This process may be periodicallyupdated to update the estimated cell center location. In addition, acheck may periodically be performed to ensure that the mobile stationsremain in an uneven distribution. The clusters may also be redefinedperiodically as mobile stations move within the cell 804.

In some cases, a mobile station may not be able to locate itself usingthe SPS positioning system because it may be located in a space thatdoes not receive wireless communications services. FIG. 9 illustrates anexample in which a cell 904 is defined by its entire cell coverage areaas a rectangle 908. The mobile stations 912 served by the cell 904 maybe found to cluster in one portion of the cell 904. A complementary area910, which is defined as the whole cell coverage area 908 minus mobilephone clustered areas 912, is illustrated in FIG. 9 as a shaded area. Itis assume that the whole cell coverage area 908 may be given as aspecification, or a parameter available to the SPS server. The center914 of the complementary area 910 may be used as an alternative locationestimate when an SPS signal is not available. In this example, when amobile station can not receive SPS signals, it may be assumed to belocated in some no-signal zones of the cell 904.

The methods described above with reference to FIGS. 5A-9 may beavailable and implemented in the cell center estimator 424 in FIG. 4.Because the methods described above with reference to FIGS. 5A and 7Bassume that the mobile stations in the cell are uniformly distributed,the cell center estimator 424 may include a method to determine if themobile stations are uniformly distributed, or uniformly distributed inclusters (e.g. FIG. 8).

It will be understood, and is appreciated by persons skilled in the art,that one or more functions, modules, units, blocks, processes,sub-processes, or process steps described above may be performed byhardware and/or software. If the process is performed by software, thesoftware may reside in software memory (not shown) in the SPS server.The software in software memory may include an ordered listing ofexecutable instructions for implementing logical functions (i.e.,“logic” that may be implemented either in digital form such as digitalcircuitry or source code or in analog form such as analog circuitry oran analog source such an analog electrical, sound or video signal), andmay selectively be embodied in any computer-readable (or signal-bearing)medium for use by or in connection with an instruction execution system,apparatus, or device, such as a computer-based system,processor-containing system, or other system that may selectively fetchthe instructions from the instruction execution system, apparatus, ordevice and execute the instructions. In the context of this document, a“computer-readable medium” and/or “signal-bearing medium” is any meansthat may contain, store, communicate, propagate, or transport theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The computer readable medium mayselectively be, for example but not limited to, an electronic, magnetic,optical, electromagnetic, infrared, or semiconductor system, apparatus,device, or propagation medium. More specific examples, but nonetheless anon-exhaustive list, of computer-readable media would include thefollowing: an electrical connection (electronic) having one or morewires, a portable computer diskette (magnetic), a RAM (electronic), aread-only memory “ROM” (electronic), an erasable programmable read-onlymemory (EPROM or Flash memory) (electronic), an optical fiber (optical),and a portable compact disc read-only memory “CDROM” (optical). Notethat the computer-readable medium may even be paper or another suitablemedium upon which the program is printed, as the program can beelectronically captured, via for instance optical scanning of the paperor other medium, then compiled, interpreted or otherwise processed in asuitable manner if necessary, and then stored in a computer memory.

1. A method for estimating a cell location for a cell that provideswireless communication services to a plurality of mobile stations eachmobile station having a Satellite Positioning System (“SPS”) receiveroperating in a positioning system, the method comprising: obtaining amobile station location for each of N mobile stations, where N isgreater than 1, having a cell identifier that identifies the cell, eachmobile station location being determined using the positioning system;and calculating an estimated location of a cell center based on astatistical measure of the mobile station location of the N mobilestations in the cell where the statistical measure is a maximumlikelihood location, wherein calculating the estimated location of thecell center based on the maximum likelihood location further comprises:obtaining a variance, σ_(tj) ², of a true position of the mobile stationj relative to a true cell center position; obtaining an SPS variance,Vj, for each mobile station, j, in the cell, calculating a cell locationvariance, V_(ij), of a true position of each mobile station j in thecell relative to the estimated cell center location as a function ofσ_(tj) ² and Vj, and using the variance, V_(ij), of each mobile stationj of N to determine the maximum likelihood location.
 2. The method ofclaim 1 including: determining if the end mobile stations are uniformlydistributed in the cell before calculating the estimated location of thecell center.
 3. The method of claim 1 further comprising the steps of:determining an initial cell radius, r₀; and setting σ_(tj) ²=(r₀/2)². 4.The method of claim 1 where the step of calculating the estimatedlocation of the cell center is based on a mean mobile station location,which further comprises: for the N mobile stations, calculating the meanusing:${{mean}\mspace{14mu}{mobile}\mspace{14mu}{station}\mspace{14mu}{location}} = {\frac{1}{N}{\sum\limits_{j = 1}^{N}{{\hat{X}}_{j}\mspace{14mu}{where}\mspace{14mu}{\hat{X}}_{j}\mspace{25mu}{is}\mspace{14mu} a\mspace{14mu}{vector}}}}$representation of each mobile station j=1 to N.
 5. A method forapproximating a current mobile station location for a mobile stationcomprising: retrieving a cell identifier for the mobile station;calculating an estimated cell center location by performing the methodof claim 1; and defining the approximate current mobile station locationto be the estimated cell center location.
 6. A non-transitory computerreadable medium having a plurality of instructions for performingprogrammed functions including the method of claim
 1. 7. A system forestimating a cell center location in a satellite positioning system(“SPS”) comprising: a SPS server connected to the SPS system to retrievea plurality of mobile station locations from mobile stations in a cellin a wireless communication system, each mobile station comprising anSPS receiver; a SPS database for storing the plurality of mobile stationlocations and a cell identifier to identify the cell in which the mobilestation is obtaining wireless communications service; and a cell centerlocation estimator for: calculating an estimated cell center location byobtaining N mobile station locations, where N is greater than 1,distributed in a cell i and calculating a statistical measure of themobile station locations, where the statistical measure is a maximumlikelihood mobile station location, determining distances between theestimated cell center location and each of the N mobile stations in thecell, determining an initial cell radius by determining the distancebetween the estimated cell center location and the mobile station thatis farthest away from the estimated cell center location, determining aminimized radius r₁ as P % of the initial cell radius, determining if P% of the N mobile stations in the cell are located within a circledefined by r₁, and if P % of the N mobile stations in the cell arelocated within a circle defined by r₁, then determining a new estimatedcell center location based on a maximum likelihood location of the P %of the N mobile stations.
 8. The system of claim 7 where the SPSdatabase stores a horizontal variance, V_(j) of each mobile stationlocation as determined by the SPS positioning system; and the cellcenter location estimator further comprises: a variance calculationfunction for calculating a variance of a true position of each of the Nmobile stations relative to an estimated cell center as a function ofV_(j); and a maximum likelihood mobile station location function forcalculating the maximum likelihood mobile station location as a functionof the variance of the true position of each of the N mobile stationsrelative to the estimated cell center location and the N mobile stationlocations.
 9. The system of claim 8 where: the variance calculationfunction calculates the variance of the true position of each of the Nmobile stations relative to the estimated cell center location using:${V_{ij} = {\begin{bmatrix}\sigma_{tj}^{2} & 0 \\0 & \sigma_{tj}^{2}\end{bmatrix} + V_{j}}},$ where σ_(tj) ² is a variance of a trueposition of the mobile station j relative to a true cell centerposition, and where σ_(tj) ²=(r₀/2)² where r₀ is the initial cellradius; and the maximum likelihood mobile station location functioncalculates the maximum likelihood mobile station location using:${\hat{X}}_{ci} = {\left\lbrack {\sum\limits_{j = 1}^{N}\; V_{ij}^{- 1}} \right\rbrack^{- 1}{\sum\limits_{j = 1}^{N}\;{V_{ij}^{- 1}{\hat{X}}_{j}}}}$for the cell i, where N is the number of mobile stations in the cell.10. The system of claim 7 where the cell center location estimatorfurther comprises a mean mobile station location function to calculate amean mobile station location of the N mobile stations.
 11. The system ofclaim 10 where the mean mobile station location function calculates themean mobile station location using:${{mean}\mspace{14mu}{mobile}\mspace{14mu}{station}\mspace{14mu}{location}} = {\frac{1}{N}{\sum\limits_{j = 1}^{N}{{\hat{X}}_{j}\mspace{14mu}{where}\mspace{14mu}{\hat{X}}_{j}\mspace{25mu}{is}\mspace{14mu} a\mspace{14mu}{vector}}}}$representation of each mobile station j=1 to N.
 12. The system of claim7 where the cell center location estimator further comprises a mobilestation location filter to find a minimum radius defining a circlearound a first estimated cell center location that includes a selectedpercentage of the N mobile station locations where the selectedpercentage of the N mobile station locations are used by the cell centerlocation estimator to calculate the estimated cell center location. 13.The system of claim 7 where the cell center location estimator furthercomprises a mobile station location filter to select a selectedpercentage of the N mobile station location that are closest to a firstestimated cell center location where the selected percentage of N mobilestations is used by the cell center location estimator to calculate asecond estimated cell center location.
 14. The system of claim 7 furthercomprising: a cluster center location estimator for defining a pluralityof clusters of mobile stations in the cell, each cluster containing anumber N_(c) of mobile stations where the cell center location estimatoris used to determine the cluster center location for N=N_(c).
 15. Anon-transitory computer readable medium having programmed instructionsfor operation in a wireless communication system that uses a satellitepositioning system (“SPS”), the computer readable medium comprising: aSPS database interface for retrieving data relating to a plurality ofmobile stations in a cell of the wireless communications system, thedata including, for each mobile station, a mobile station location and acell identifier to identify the cell in which the mobile station isobtaining wireless communications service; and a plurality of programmedinstruction for: calculating an estimated cell center location byobtaining N mobile station locations, where N is greater than 1,distributed in a cell i and calculating a statistical measure of themobile station locations, where the statistical measure is a maximumlikelihood mobile station location, determining distances between theestimated cell center location and each of the N mobile stations in thecell, determining an initial cell radius by determining the distancebetween the estimated cell center location and the mobile station thatis farthest away from the estimated cell center location, determining adistance between the estimated cell center location and the mobilestation that is closest to a radius r1 that defines a circle containingP % of the N mobile stations in the cell, and determining a newestimated cell center location based on the maximum likelihood locationof the P % of the N mobile stations.
 16. The computer readable mediumaccording to claim 15 where the SPS database stores a horizontalvariance, V_(j) of each mobile station location as determined by the SPSpositioning system; and the computer readable medium further comprises:a second plurality of programmed instructions for calculating a varianceof a true position of each of the N mobile stations relative to anestimated cell center as a function of V_(j); and a third plurality ofprogrammed instructions for calculating the maximum likelihood mobilestation location as a function of the variance of the true position ofeach of the N mobile stations relative to the estimated cell centerlocation and the N mobile station locations.
 17. The computer readablemedium according to claim 15 further comprising a fourth plurality ofprogrammed instructions to calculate a mean mobile station location ofthe N mobile stations.
 18. The computer readable medium according toclaim 15 further comprising a fifth plurality of programmed instructionsto find a minimum radius defining a circle around a first estimated cellcenter location that includes a selected percentage of the N mobilestation locations where the selected percentage of the N mobile stationlocations are used by the cell center location estimator to calculatethe estimated cell center location.
 19. The computer readable mediumaccording to claim 15 further comprising a sixth plurality of programmedinstructions to select a selected percentage of the N mobile stationlocation that are closest to a first estimated cell center locationwhere the selected percentage of N mobile stations is used by the cellcenter location estimator to calculate a second estimated cell centerlocation.
 20. The computer readable medium according to claim 15 furthercomprising: a seventh plurality of programmed instructions for defininga plurality of clusters of mobile stations in the cell, each clustercontaining a Number N_(c) of mobile stations where the plurality ofprogrammed instruction for calculating the estimated cell centerlocation is used to determine the cluster center location for N=N_(c).21. An apparatus in a satellite positioning system (“SPS”) comprising: afirst interface to a SPS database for retrieving from storage in the SPSdatabase a plurality of mobile station locations corresponding to aplurality of mobile stations operating in a cell of the wirelesscommunication system and a cell identifier to identify the cell in whichthe mobile station is obtaining wireless communications service; and acell center location estimator for: calculating an estimated cell centerlocation by obtaining N mobile station locations, where N is greaterthan 1, distributed in a cell i and calculating a statistical measure ofthe mobile station locations, where the statistical measure is a maximumlikelihood mobile station location, and testing the mobile stationlocations to determine if the mobile stations are clustered by:determining an initial cell radius, defining a plurality of circleshaving radii less than the initial cell radius with centers at randomlocations in the cell, determining if each of the plurality of circlesdefines an area containing a cluster of uniformly distributed mobilestation locations, and for each of the plurality of circles that definesa cluster of uniformly distributed mobile station locations, determiningan estimated cluster center location based on a maximum likelihoodlocation of the mobile stations in the cluster.
 22. The apparatus ofclaim 21 where the first interface to the SPS database retrieves ahorizontal variance, V_(j) of each mobile station location as determinedby the SPS positioning system; and the cell center location estimatorfurther comprises: a variance calculation function for calculating avariance of a true position of each of the N mobile stations relative toan estimated cell center as a function of V_(j); and a maximumlikelihood mobile station location function for calculating the maximumlikelihood mobile station location as a function of the variance of thetrue position of each of the N mobile stations relative to the estimatedcell center location and the N mobile station locations.
 23. Theapparatus of claim 21 where the cell center location estimator furthercomprises a mean mobile station location function to calculate a meanmobile station location of the N mobile stations.
 24. The apparatus ofclaim 21 where the cell center location estimator further comprises amobile station location filter to find a minimum radius defining acircle around a first estimated cell center location that includes aselected percentage of the N mobile station locations where the selectedpercentage of the N mobile station locations are used by the cell centerlocation estimator to calculate the estimated cell center location. 25.The apparatus of claim 21 where the cell center location estimatorfurther comprises a mobile station location filter to select a selectedpercentage of the N mobile station location that are closest to a firstestimated cell center location where the selected percentage of N mobilestations is used by the cell center location estimator to calculate asecond estimated cell center location.
 26. The apparatus of claim 21further comprising: a cluster center estimator for defining a pluralityof clusters of mobile stations in the cell, each cluster containing anumber N_(c) of mobile stations where the cell center location estimatoris used to determine the cluster center location for N=N_(c).